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Down is the "absolute" status effect in most RPG games. When a character's HP reaches zero, they fall in battle, then lay motionless on the ground. A downed party member cannot attack or use any commands. After a battle is won, any downed party members are restored to 1 HP (except Paper Mario: The Thousand-Year Door, where that HP remains zero), excluding bosses, when all party members are restored to full HP after being defeated.
Super Mario RPG: Legend of the Seven Stars
Party members are effectively out of the battle unless they are revived, either via a Pick Me Up or Princess Toadstool's Come Back technique. If all three party members are downed in battle, it is Game Over.
Mario & Luigi series
When a brother's HP reaches zero, he falls in battle, and then is no longer able to battle until he is revived via a 1-Up Mushroom, a 1-Up DX or in the case of Mario & Luigi: Paper Jam, a Double 1-Up Mushroom. While a brother is defeated, the other brother will carry them on their back on the enemy's turn, slowing them down and making it harder to dodge, and they will not be able to perform any Bros. Attacks, Bros. Items (Mario & Luigi: Partners in Time; if a certain item requires two or all four characters), Special Attacks (Mario & Luigi: Bowser's Inside Story), or Trio Attacks (Mario & Luigi: Paper Jam). When running away from battle, the defeated brother will be carried on the still-standing brother's back while they run away. In the case of all four characters are fighting together in Mario & Luigi: Partners in Time, when the older brother falls, their respective baby counterpart will carry them out of the scene. In the case of when characters, like Paper Mario, fall in battle, Mario and Luigi will not carry them. When all characters fall in battle, the player will receive a Game Over.
Paper Mario: The Thousand-Year Door
A downed partner's HP is not recovered to 1 HP after a battle is won, excluding all bosses except Shadow Queen, when all partners are restored to full HP after falling in battle.
If Mario's HP reaches zero with no Life Shrooms, then he will be down and receive a Game Over.